# Optimal and robust noncausal filter formulations

@article{Einicke2006OptimalAR,
title={Optimal and robust noncausal filter formulations},
author={Garry A. Einicke},
journal={IEEE Transactions on Signal Processing},
year={2006},
volume={54},
pages={1069-1077}
}
• G. Einicke
• Published 1 March 2006
• Mathematics
• IEEE Transactions on Signal Processing
The paper describes an optimal minimum-variance noncausal filter or fixed-interval smoother. The optimal solution involves a cascade of a Kalman predictor and an adjoint Kalman predictor. A robust smoother involving H/sub /spl infin// predictors is also described. Filter asymptotes are developed for output estimation and input estimation problems which yield bounds on the spectrum of the estimation error. These bounds lead to a priori estimates for the scalar /spl gamma/ in the H/sub /spl infin…
33 Citations

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## References

SHOWING 1-10 OF 40 REFERENCES
H/sub infinity /-minimum error state estimation of linear stationary processes
A state estimator is derived which minimizes the H/sub infinity /-norm of the estimation error power spectrum matrix. Two approaches are presented. The first achieves the optimal estimator in the
Robust steady-state filtering for systems with deterministic and stochastic uncertainties
• Computer Science, Mathematics
IEEE Trans. Signal Process.
• 2003
This work presents filtering algorithms that solve each of these problems, with the filter parameters determined via convex optimization based on linear matrix inequalities, and demonstrates the performance of these robust algorithms on a numerical example consisting of the design of equalizers for a communication channel.
Robust extended Kalman filtering
• Engineering
IEEE Trans. Signal Process.
• 1999
A new approach to the robust design of a discrete-time EKF is presented by application of the robust linear design methods based on the H/sub /spl infin// norm minimization criterion to demonstrate an advantage for signal demodulation and nonlinear equalization applications.
On discrete-time H∞ fixed-lag smoothing
• Mathematics, Computer Science
• 2004
Efficient algorithms are worked out that permit checking of solvability and implementation of the smoother, relying only on the solution of the H∞ filtering Riccati equation, which provides a fast method to compute the minimum lag guaranteeing a desired attenuation level.
On discrete-time H/sub /spl infin// fixed-lag smoothing
• Mathematics, Computer Science
IEEE Transactions on Signal Processing
• 2004
Efficient algorithms are worked out that permit checking of solvability and implementation of the smoother, relying only on the solution of the H/sub /spl infin// filtering Riccati equation, which provides a fast method to compute the minimum lag guaranteeing a desired attenuation level.
Filtering and smoothing in an H/sup infinity / setting
• Mathematics
• 1991
The problems of filtering and smoothing are considered for linear systems in an H/sup infinity / setting, i.e. the plant and measurement noises have bounded energies (are in L/sub 2/), but are
The use of fake algebraic Riccati equations for co-channel demodulation
• Engineering
IEEE Trans. Signal Process.
• 2003
A method for nonlinear filtering based on an adaptive observer, which guarantees the local stability of the linearized error system and is compared with an EKF for a co-channel frequency demodulation application.
The independance of forward and backward estimation errors in the two-filter form of the fixed interval Kalman smoother
In this paper it is shown that the Fraser-Potter two-filter form of the fixed interval Kalman smoother can be derived without assuming that the forward and backward estimation errors are independent.
An innovation approach to H∞ fixed-lag smoothing for continuous time-varying systems
• Mathematics
IEEE Trans. Autom. Control.
• 2004
A technique named as reorganized innovation analysis in Krein space is developed to give a necessary and sufficient condition for the existence of an H/sub /spl infin// fixed-lag smoother.